New remarkable ko beast?

[Criado]

(A shrinked copy for fun )

$$B
$$ --------------
$$ | O . O . X X X |
$$ | X O O X X . . |
$$ | X . X O O O O |
$$ | X X X . O O O |
$$ ----------------

Click Here To Show Diagram Code

[go]$$B
$$ --------------
$$ | O . O . X X X |
$$ | X O O X X . . |
$$ | X . X O O O O |
$$ | X X X . O O O |
$$ ----------------[/go]

Cute board!

Thanks. This small board could actually make a nicer diagram than the current 0-sided ko placeholder on the RR page. Would you mind if I use it there (crediting you oc)?

Sure! go ahead. Please credit us as Francisco Criado and René Martínez. Also, for the page on unremovable ko for both sides I will add the original diagram, it's my personal preference to not use small boards for examples (but I see why someone else might prefer the way you did it).

[kvasir]

Now, this definition involves a limit as d->0 of the scores (they are actually called "stops" in the CGT literature, but in go "score" feels more like the final score. So when I talk about go I prefer to use "thermograph" for what they call "scores" and "scores" for what they call "stops") of a game of the form G+E_t^d +-t/2. Now, my claim is that this limit is of course not defined as we already discussed, the function is very discontinuous and does not converge to anything.

The way this discussion is going I think maybe you should write to the author of the book with the question as to when it applies. You seem to be very interested in this as presented in their book.

After viewing your diagrams I suspect that you have constructed the CGT game in a way that doesn't allow a thermography. You said Chinese rules, which do forbid repeated positions (but arguably they say one thing when discussing rules for players and a different thing when discussing rules for referees) and the game could arguably end as-is in these positions. If the ko rule forbids the recapture in these positions they are only "hot" if the other player has a move (a ko threat) and otherwise the Go game is over because both players pass. At least that is my interpretation.

Like I said, I don't see what is special about the position when it comes to converting to a CGT game and plotting a thermography. One player is the last one to capture the ko, the other player has no legal move they wish to make and has to allow the game to end. I have a rules interpretation in mind and don't see why the CGT game would not have a nice thermography, I am not sure what your idea is.

[jann]

You said Chinese rules, which do forbid repeated positions (but arguably they say one thing when discussing rules for players and a different thing when discussing rules for referees) and the game could arguably end as-is in these positions. If the ko rule forbids the recapture in

Taking the (poorly) written text too literally seems bad idea here (and even that shows repetition in triple ko = draw as example). Actual practice seems more relevant, and afaik in China even most amateurs are aware of the "no win no loss" rule - let alone pros in official games. This isn't really in conflict with the text either, which forbids repetition in some shapes while allowing repetition in others.

Imo the Chinese ruling on recapture in 0-sided kos would likely match the ruling on 1-eye-flaw. The original author of that page claims Chinese rules do allow recapture there (without citing references though). But this at least seems plausible considering the uniform repetition / triple ko treatment and common sense among Asian rules.

[Criado]

Now, this definition involves a limit as d->0 of the scores (they are actually called "stops" in the CGT literature, but in go "score" feels more like the final score. So when I talk about go I prefer to use "thermograph" for what they call "scores" and "scores" for what they call "stops") of a game of the form G+E_t^d +-t/2. Now, my claim is that this limit is of course not defined as we already discussed, the function is very discontinuous and does not converge to anything.

The way this discussion is going I think maybe you should write to the author of the book with the question as to when it applies. You seem to be very interested in this as presented in their book.

I'm not particularly interested in their book per se, but it is the only place I know of (and I have checked the source material) that at least has an attempt at formally defining and mathematically proving the results on loopy thermography. For the non-loopy case there is ONAG and winning ways. Same for go, many people can draw thermographs and compute move values for simple loopy go positions. But without a formal definition there is no hope to compute them automatically. And my goal would be to have some software that can compute move values for any endgame position in go under various komaster/monster assumptions and ko ban rules.

Like I said, I don't see what is special about the position when it comes to converting to a CGT game and plotting a thermography. One player is the last one to capture the ko, the other player has no legal move they wish to make and has to allow the game to end. I have a rules interpretation in mind and don't see why the CGT game would not have a nice thermography, I am not sure what your idea is.

Well what makes the position special is that the ko is decided almost by luck, whoever gets lucky enough to take the last coupon wins or loses, but the number of coupons is a variable as d->0. Then the thermograph cannot be continuous should it be defined as in some temperatures one player wins, in others extremely close ones the other player wins. However the continuity of thermographs is a straightforward consequence of its definition.

I mean, a pass fight like this will make the thermograph undefined in either go or CGT. This is because adding a * (a dame) will change the outcome of the game at higher temperatures as we discussed. The Orthodox Forecast Theorem says that in the presence of a rich environment of t large enough, the expected score of a game of the form G+H+E_t with Left playing first should be m(G)+m(H)+t/2. Since * has mast value 0, then it should be the case that m(G)+m(*)+t/2 = m(G)+t/2. However we saw that the addition of a * can alter the score by several points.

Even without using the Orthodox Theorems, which are heavy machinery, it is true in general that for any t>0, the thermograph of G should coincide with that of G+*.

[kvasir]

Taking the (poorly) written text too literally seems bad idea here (and even that shows repetition in triple ko = draw as example). Actual practice seems more relevant, and afaik in China even most amateurs are aware of the "no win no loss" rule - let alone pros in official games. This isn't really in conflict with the text either, which forbids repetition in some shapes while allowing repetition in others.

Maybe, the Chinese rules are obviously not meant to be a computer program. This thing is not the only thing that the "rules for players" and "rules for referees" appear to differ about. Actual practice is something that can and does change, it is also difficult for referees to validate superko claims. It is obviously interesting but if you want to discuss CGT then you need to make sure you are working with a representation that is a CGT game.

Well what makes the position special is that the ko is decided almost by luck, whoever gets lucky enough to take the last coupon wins or loses, but the number of coupons is a variable as d->0. Then the thermograph cannot be continuous should it be defined as in some temperatures one player wins, in others extremely close ones the other player wins. However the continuity of thermographs is a straightforward consequence of its definition.

I think if A,B,C and D are numbers then game G := {{A|B}|{C|D}} is G = {B|C} when the temperature is sufficiently small or otherwise {A|B} and/or {C|D} are numbers. It is just an intuitive understanding but provided that some conditions are not violated the games represented by the left and right walls of the thermography will simplify at lower temperatures. Cycles are also treated as draws in CGT as far as I know, so I don't see the problem when the ko cycle is so clean (but you need to decide how to model it). I don't see how any space-filling curves can be involved because the games on the left and right walls (in the thermography plot) simplify.

To put it simply in other words: play is forced at low temperatures.

[jann]

... This is because adding a * (a dame) will change the outcome of the game at higher temperatures
... Since * has mast value 0, then it should be the case that m(G)+m(*)+t/2 = m(G)+t/2.
... in general that for any t>0, the thermograph of G should coincide with that of G+*.

As I said I'm not sure if I follow the CGT part. To get this no-pass-go behavior (where dame may change things) you need a somewhat no-pass ruleset. This means strict superko (where pass lift no ban), which basically excludes Asian CJK rules and means AGA/NZ only. But AGA uses area scoring, where a dame is valuable. Is it still a * then? And (while moves into territory do matter in that case), how does adding a dame change the outcome if the side who can first capture the ko will only do that after filling all dame? (cf. molasses ko under PSK - another known no-pass-go case - where such postpone is not possible)

From a rules view, 1-eye-flaw is only problem for strict superko, since all it shows is the importance of passes as whole / fully functional moves. Otoh 0-sided kos can be challenging even with complete passes, as a repetition that needs to be recognized despite spanning stops - while at the same time similar repetition with a double ko seki (without score changes) should not.

I'm not sure how can the CGT view handle (if at all) 0-sided kos under normal, everyday rules where passes do lift bans. But in this case (if the score is otherwise close enough) moves into the position gain nothing regardless of temperature, since the outcome is still draw on repetition even if I omit or postpone my next capture (the opponent can do nothing to prevent that later with or without resumption).

[jann]

Your original post was just bumped by dhu163, and it seems to shed some light on the logical problem:

positional super ko (the standard in CGT) ... Recall that in this context, passing does not lift ko bans but playing an environment play does.

This doesn't seem like a reasonable start. In particular, environmental plays seem hard to use correctly in relation to a superko game - assuming the environment is supposed to offer a finely granulated transition from more valuable plays/coupons down to zero.

Under strict superko (where they don't lift bans), "passes" are not the same infinite, zero-valued but otherwise fully functional, environmental-coupon-compatible moves as in modern go (where they do lift bans, except for AGA/NZ). And an environmental stack cannot form a continuous bridge from high-valued ban-lifting moves down to near-zero-valued NON-ban-lifting move.

(Bill's idea / workaround rule for how to allow passes to lift superko ban may also be relevant here, but it has its own problems and also doesn't seem to solve 0-sided kos.)

[luigi]

Is it the case that, in No-Pass Go with prisoner return, if there are no situations that invite repetitions, the winner in this position is simply the player with the greater sum of territory and prisoners, with the provisions that the ko intersection be counted as territory for the opponent and half a point be subtracted from the player to move?